Safonov, K. V. On algebraicity and rationality conditions of the sum of a power series. (Russian) Zbl 0622.32009 Mat. Zametki 41, No. 3, 325-332 (1987). It is shown that a convergent series \(f(z)=\sum_{k\geq 0}\alpha_ kz^ k\) defines a rational function iff there is a rational function \(F(z_ 1,z_ 2)=\sum_{m,n\geq 0}a_{mn}z^ m_ 1z^ n_ 2\) such that \(\sum_{k}\alpha_ kz^ k=\sum_{k}a_{kk}z^ k\). Reviewer: A.Pankov Cited in 1 ReviewCited in 3 Documents MSC: 32B05 Analytic algebras and generalizations, preparation theorems 32A05 Power series, series of functions of several complex variables Keywords:convergent power series; rational function PDFBibTeX XMLCite \textit{K. V. Safonov}, Mat. Zametki 41, No. 3, 325--332 (1987; Zbl 0622.32009)